Question

8. The length and
breadth of a rectangular piece of land are in the ratio of 5:3. If the totales
of fencing it at 24 per metre is 9600 find its length and breadth.​

Answer 1

Given :-

Ratio of the length and breadth of the land = 5 : 3

Total cost of fencing the land at Rs. 24 per meter = 9600

To Find :-

The length of the rectangle.

The breadth of the rectangle.

Analysis :-

First find the perimeter of the land.

Then consider the common ratio as 'x' and length and breadth would be 5x and 3x respectively.

Make an equation and solve x.

Substitute the value of x in length and breadth given and solve it.

Solution :-

We know that,

• l = Length
• b = Breadth
• p = Perimeter

Finding the perimeter,

$\underline{\boxed{\sf Perimeter=Total \ cost \ of \ fencing \div Cost \ per \ meter }}$

Substituting their values,

Perimeter = 9600 ÷ 24

Perimeter = 400 m

Therefore, perimeter is 400 meter.

Let the common ratio be 'x'. Then the length and breadth would be '5x' and '3x' respectively.

According to the question,

$\underline{\boxed{\sf Perimeter=2(Length+Breadth)}}$

Substituting them,

Perimeter = 2(5x + 3x) = 400

Perimeter = 16x = 400

Finding the value of x,

x = 400/16

x = 25

The value of x is 25.

Length = 5x

Length = 5 × 25 = 125 m

Therefore, the length is 125 m

Breadth = 3x

Breadth = 3 × 25 = 75 m

Therefore, the breadth is 75 m